The criterion evaluation matrix.

Probabilistic hesitant fuzzy sets (PHFSs) are superior to hesitant fuzzy sets (HFSs) in avoiding the problem of preference information loss among decision makers (DMs). Owing to this benefit, PHFSs have been extensively investigated. In probabilistic hesitant fuzzy environments, the correlation coefficients have become a focal point of research. As research progresses, we discovered that there are still a few unresolved issues concerning the correlation coefficients of PHFSs. To overcome the limitations of existing correlation coefficients for PHFSs, we propose new correlation coefficients in this study. In addition, we present a multi-criteria group decision-making (MCGDM) method under unknown weights based on the newly proposed correlation coefficients. In addition, considering the limitations of DMs’ propensity to use language variables for expression in the evaluation process, we propose a method for transforming the evaluation information of the DMs’ linguistic variables into probabilistic hesitant fuzzy information in the newly proposed MCGDM method. To demonstrate the applicability of the proposed correlation coefficients and MCGDM method, we applied them to a comprehensive clinical evaluation of orphan drugs. Finally, the reliability, feasibility and efficacy of the newly proposed correlation coefficients and MCGDM method were validated.